Question

Two parallel and opposite forces, each of magnitude 4000 N, are applied tangentially to the upper and lower faces of a cubical metal block 25 cm on a side. Find the angle of shear and the displacement of the upper surface relative to the lower surface. The shear modulus for the metal is 80 GPa.

Answer 1

We use the approximate from S = Fl(A$\varphi$)
Putting S = 8 $\times {10}^{10}N/m^2$, F = 4000 N and A = $(0.25{)}^2$ = 6.25 $\times {10}^{-2}{m}^2$ in above equation and solving for $\varphi$, we get
$\varphi =\frac{\left(4000N\right)}{(6.25\times {10}^{-2}{m}^2)(8\times {10}^{10}N/m^2)}=0.8\times {10}^{-7}rad$
The displacement of the upper surface is given by d = L$\varphi$, where L is an edge of the cube.
$\therefore d=(8.0\times {10}^{-7})\left(25cm\right)=2.0\times {10}^{-5}cm$